Problem: Solve for $x$ and $y$ using substitution. ${-2x-2y = -6}$ ${y = -3x-1}$
Since $y$ has already been solved for, substitute $-3x-1$ for $y$ in the first equation. ${-2x - 2}{(-3x-1)}{= -6}$ Simplify and solve for $x$ $-2x+6x + 2 = -6$ $4x+2 = -6$ $4x+2{-2} = -6{-2}$ $4x = -8$ $\dfrac{4x}{{4}} = \dfrac{-8}{{4}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -3x-1}\thinspace$ to find $y$ ${y = -3}{(-2)}{ - 1}$ $y = 6 - 1$ $y = 5$ You can also plug ${x = -2}$ into $\thinspace {-2x-2y = -6}\thinspace$ and get the same answer for $y$ : ${-2}{(-2)}{ - 2y = -6}$ ${y = 5}$